Equality among Unequals

This paper establishes an equivalence between three incomplete rankings of distributions of income among agents that are vertically differentiated with respect to some other non-income characteristic (health, household size, etc.). The first ranking is that associated with the possibility of going from one distribution to the other by a finite sequence of income transfers from richer and more highly ranked agents to poorer and less highly ranked ones. The second ranking is the unanimity of all comparisons of two distributions made by a utilitarian planer who assumes that agents convert income into utility by the same function exhibiting a marginal utility of income that is decreasing with respect to both income and the source of vertical differentiation. The third ranking is the Bourguignon (1989) ordered poverty gap dominance criterion.